Order 13568.
668 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20273503 | C2 | semidirect |
| 4. #20273498 | C2 | semidirect |
| 5. #20273461 | C2 | semidirect |
| 21. #16810375 | C22 | semidirect |
| 22. #16810373 | C22 | semidirect |
| 210. C53 | #17806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283348 | 2 |
| C2×#16810676 | 2 |
| #20273503 | 2 |
| #20273498 | 2 |
| #20273461 | 2 |
| C2×C53×#431 | 2 |
| #17806 | 53 |